CN105678086A - Alternate iterative algorithm for temperature field and concentration field reconstruction based on spectral absorption - Google Patents

Abstract

The invention discloses an alternate iterative algorithm for reconstruction of temperature field and concentration field based on spectral absorption. First, a linearization scheme is proposed for the calculation of concentration field, and the original system is semi-linearized, thereby weakening the nonlinearity of the original system; secondly An alternate iteration scheme is proposed for the measured temperature field and concentration field, and the number of unknown variables is reduced by half in each step of iteration; finally, a penalty term is introduced by optimization technology to overcome the ill-conditioned nature of the reconstruction process, and the regularization can be automatically adjusted in each step of iteration parameter, which ensures that the iterative solution converges to the exact solution. The alternate iteration scheme proposed by the invention can significantly shorten the calculation time under the premise of maintaining the reconstruction accuracy, and is suitable for large-scale field inversion calculation.

Description

An Alternate Iterative Algorithm for Reconstruction of Temperature Field and Concentration Field Based on Spectral Absorption

technical field

The invention relates to an alternate iterative algorithm for reconstruction of temperature field and concentration field based on spectral absorption, belonging to the field of laser absorption spectroscopy.

Background technique

In recent years, with the country's increasing emphasis on environmental protection and the need to ensure safe and efficient industrial production, optical non-contact gas detection technology has developed rapidly. Gas detection technology based on laser absorption spectroscopy has the advantages of no preprocessing, fast response, accurate data, and simultaneous detection of multiple parameters, and has become one of the on-site on-line detection technologies currently used in many fields.

Absorption spectroscopy technology uses a laser to pass through the area of the flow field to be measured. When the laser frequency is the same as the transition frequency of the gas absorption component, the laser energy will be absorbed. By comparing the incident light intensity with the transmitted light intensity, the absorption value along the optical path can be obtained. , and then determine the physical parameters such as gas temperature and concentration. However, the measurement results of laser absorption spectroscopy reflect the average temperature or concentration of an area, which is not suitable for measurement environments with significant temperature and concentration gradients. Therefore, it is of great significance to explore and develop the measurement method of non-uniform flow field parameters based on absorption spectroscopy.

At present, scientific research institutions at home and abroad have carried out some research on the measurement of non-uniform field parameter distribution of high-temperature reaction flow, and the measurement methods based on different principles have their own advantages and disadvantages. The limited-range direct reconstruction method uses basis functions to discretize the measured area, which is suitable for smooth distribution of the flow field, but not suitable for the situation where there is a sudden change in the measured area. The filtered back-projection algorithm can obtain high-precision reconstruction results under a large number of projection rays and uniform projection angles, but the angle and number of projection rays are limited by space availability and system complexity in actual combustion field measurements. The algebraic iterative algorithm is an optimization algorithm based on an iterative solution strategy. It can be used for incomplete projection data or projections with non-uniform distribution. The calculation speed is fast, but it needs to increase the number of projections in different directions and cannot be used at the same time. Information about multiple absorption lines. The sequential quadratic programming algorithm has overall convergence while maintaining local super-1 convergence, and has high search efficiency, but it is extremely sensitive to the initial value, and it is easy to fall into the local optimum and fail to obtain the global optimal solution. The simulated annealing algorithm improves the accuracy and stability of the temperature field and concentration field reconstruction results by increasing the measured value of the gas absorption spectrum on a single optical path. The overall reconstruction effect is better than the above algorithm, but it belongs to the random search optimization algorithm, and the calculation efficiency is low. , Time-consuming.

Contents of the invention

The technical problem to be solved by the present invention is to provide an alternate iterative algorithm for reconstruction of temperature field and concentration field based on spectral absorption.

In order to solve the problems of the technologies described above, the technical scheme adopted in the present invention is as follows:

An alternate iterative algorithm for reconstruction of temperature field and concentration field based on spectral absorption, including the following steps:

Step 1, the high-temperature gas to be measured flows through a two-dimensional rectangular area, and the area to be measured is recorded as D={(x, y): 0<x<L, 0<y<W}, and the temperature field is T(x, y ), the concentration field is X(x, y), the relationship between the measured value of the laser passing through area D and the temperature field and concentration field in area D is expressed by formula (1):

where A(y ₀ , v ₀ ) is the measured value of the integrated absorption area of the incident laser with center frequency v ₀ along the path y=y ₀ ∈ (0, W), B(x ₀ , v ₀ ) is the x = x ₀ ∈ (0, L) integral absorption area measurement, P is the gas pressure on region D, S(T(x, y ₀ ), v ₀ ) is the temperature T(x, y ₀ ), the intensity of the spectral line at frequency v ₀ ;

Step 2. Solve (X(x, y), T(x, y)) according to formula (1):

1) Assume that (X ^* (x, y), T ^* (x, y)) is an exact solution that satisfies the system, and give (X ^* (x, y), T ^* (x, y)) a prior Proximity And the initial value of iteration (X ⁰ (x, y), T ⁰ (x, y)), and give the maximum number of iterations N _max , regularization parameter μ, β>0, iteration termination level ε>0 and the allowable set X _range ×T _range , set the initial value of n to 0;

2) For the known T ⁿ (x, y), X ⁿ⁺¹ (x, y) can be obtained by regularizing the following formula after discretization:

In the formula, Indicates the operator used during iteration; if X ⁿ⁺¹ (x, y)∈X _range , take μ=μ ₀ and jump out of this iteration; otherwise update μ←2μ, and calculate X ⁿ⁺¹ (x, y) again ;

3) For the known X ⁿ⁺¹ (x, y), T ⁿ⁺¹ (x, y) can be obtained by regularizing the following formula after discretization:

In the formula, Indicates the operator used during iteration; if T ⁿ⁺¹ (x, y)∈T _range , take β=β ₀ and jump out of this iteration, otherwise update β←2β, and calculate T ⁿ⁺¹ (x, y) again ;

4) For a sufficiently large number n, the termination criterion is met:

||(X ⁿ⁺¹ ，T ⁿ⁺¹ )-(X ⁿ ，T ⁿ )|| _D ＜ε(4);

or n=N _max , the iteration terminates, and (X ⁿ⁺¹ , T ⁿ⁺¹ ) is used as the final solution of the concentration field and temperature field; otherwise, update T ⁿ ←T ⁿ⁺¹ , n←n+1, and repeat step 2)～ 4).

In order to improve the reconstruction effect, the present invention proposes to make full use of the information including multiple gas characteristic absorption lines in each direction of the region to be measured, and select the center frequency corresponding to the rth gas characteristic absorption line as v _r , Equation (2.1), Equation (2.2), Equation (3.1), Equation (3.2) and (A, B) depend on v _r , so Equation (2.1), Equation (2.2), Equation (3.1) and Equation (3.2) Each step of iteration can be replaced by formula (5.1), formula (5.2), formula (6.1) and formula (6.2):

Perform grid discretization in the two-dimensional area to be measured, and use an adaptive iterative method to solve the concentration and temperature in each grid, that is, X ⁿ⁺¹ (x, y) and T ⁿ⁺¹ (x, y) :

1) According to the shape and size of the two-dimensional area D to be measured, divide the two-dimensional area to be measured into grids of M rows and N columns, let M=N, and each grid corresponds to a concentration and temperature to be measured , select I gas characteristic absorption line from spectral database, and I≥[2×M×N/(M+N)], the value of r is an integer between 1 and 1;

2) Formula (5.2) is written as:

EgS(T,v _r )X=P(v _r )(7);

In the formula, P(v _r ) is the measured value projection vector corresponding to the spectral line v _r , E=(e( _{i, j)} ) is a 2N×N ² -dimensional 0-1 matrix, where e _{(i, j)} represents Whether the laser passes through the j-th grid in the i-th direction; that is, when the laser in the i-th direction passes through the j-th grid, let e _{(i, j)} = 1, otherwise e _{(i, j)} = 0;

The explicit solution of formula (7) is expressed as:

in,

Through formula (8), X ⁿ⁺¹ (x, y) can be calculated from T ⁿ (x, y);

3) X ⁿ⁺¹ (x, y) calculated from step 2) is used as a known quantity, and T ⁿ⁺¹ (x, y) can be obtained by solving formula (6.1) using nonlinear least squares optimization algorithm.

In order to ensure the numerical convergence of the iterative solution, the admissible set X _range ×T _range of X(x, y) and T(x, y) is given, so that it contains the exact solution X ^* (x, y) and T ^* (x, y), while introducing penalties with regularization parameters μ, β to overcome the ill-conditioned nature of the reconstruction process, and automatically adjust the regularization parameters μ, β in each step of iteration, so as to ensure that the iterative solution converges to the exact solution.

Beneficial effects: the algorithm of the present invention can solve the non-linear problem when using absorption spectrum data to reconstruct the temperature field and concentration field, and at the same time use optimization technology to introduce penalty items to overcome the ill-conditionedness in the reconstruction process, not only can make full use of multi-spectral measurement information, Moreover, the calculation time can be significantly shortened while maintaining the reconstruction quality.

Description of drawings

Fig. 1 is the flowchart of algorithm of the present invention;

Fig. 2 is the schematic diagram of the grid division of the region to be measured in the algorithm of the present invention;

Fig. 3 is the concentration field model diagram set in the simulation embodiment of the present invention;

Fig. 4 is the temperature field model diagram of setting in the simulation embodiment of the present invention;

Fig. 5 is the result figure of the algorithm reconstruction concentration field of the present invention;

Fig. 6 is the result figure of the algorithm reconstruction temperature field of the present invention;

Fig. 7 is the result diagram of reconstructing the concentration field by the simulated annealing algorithm;

Fig. 8 is a result diagram of reconstructing the temperature field by the simulated annealing algorithm;

Fig. 9 is the root mean square error diagram of the reconstruction temperature field under different noise levels by the algorithm proposed by the present invention and the simulated annealing algorithm.

detailed description

The present invention will be described in detail below in conjunction with the accompanying drawings.

As shown in Figure 1, the present invention is based on the alternating iterative algorithm of spectral absorption temperature field and concentration field reconstruction, including the following implementation steps:

Step 1. Assuming that the high-temperature gas to be measured flows through a two-dimensional rectangular area, lasers of different frequencies are incident from the side of the area, and the corresponding lasers absorbed by the gas are obtained on the opposite side, and the area to be measured is recorded as D={(x , y): 0<x<L, 0<y<W}, the temperature field is T(x, y), the concentration field is X(x, y), and the center frequency corresponding to the gas characteristic absorption line is v ₀ . The energy absorption along the optical path y = y ₀ ∈ (0, W) is expressed as:

In the formula, I(L, y ₀ , v ₀ ) is the transmitted light intensity obtained at x=L along y=y ₀ , corresponding to the laser incident light intensity I(0, y ₀ , v ₀ ); α( y ₀ , v, v ₀ ) is the absorbance of the incident laser at the path y=y ₀ ; P is the gas pressure on the area D; φ(vv ₀ ) is the line function corresponding to the selected spectral line at the frequency v Value, according to the temperature and pressure conditions in the measurement environment, choose one of the Gauss line type, Lorentz line type and Voigt line type, and satisfy S(T(x, y ₀ ), v ₀ ) is the spectral line intensity at temperature T(x, y ₀ ) and frequency v ₀ , which can be expressed as:

In the formula, the reference temperature T ₀ =296K, h is Planck’s constant, c is the speed of light, E″ is the low-state energy level, and k is Boltzmann’s constant. The molecular partition function Q(T) is approximately described as:

Q(T)=a+bT+cT ² +dT ³ (3);

The coefficients (a, b, c, d) depend on the temperature range to which they belong;

Then the integrated absorption area along the light path y=y ₀ ∈ (0, W) is expressed as:

Similarly, energy absorption along the light path x = x ₀ ∈ (0, L) satisfies:

The integrated absorption area along this path is then expressed as:

Among them, the values of A(y ₀ , v ₀ ) and B(x ₀ , v ₀ ) can be obtained through experiments;

Step 2, by solving formula (7):

The concentration field X(x, y) and temperature field T(x, y) in the area D can be obtained; observing the system, it can be concluded that:

1) Although formula (7) is nonlinear with respect to (X(x, y), T(x, y)), if T(x, y) is given, then formula (7) with respect to X(x, y) is linear;

2) For a given T(x, y), formula (7) is unstable with respect to X(x, y), that is, a small disturbance of (A, B) will cause X(x, y) to be very large The change;

3) For a given X(x, y), formula (7) is still nonlinear with respect to T(x, y);

According to the characteristics of the system, solve (X(x, y), T(x, y)):

1) Assume that (X ^* (x, y), T ^* (x, y)) is an exact solution that satisfies the system, and give (X ^* (x, y), T ^* (x, y)) a prior Proximity And the initial value of iteration (X ⁰ (x, y), T ⁰ (x, y)), and give the maximum number of iterations N _max , regularization parameter μ, β>0, iteration termination level ε>0 and the allowable set X _range ×T _range , set the initial value of n to 0;

2) For the known T ⁿ (x, y), X ⁿ⁺¹ (x, y) can be obtained by regularizing the following formula after discretization:

In the formula, Indicates the operator used during iteration; if X ⁿ⁺¹ (x, y)∈X _range , take μ=μ ₀ and jump out of this iteration; otherwise update μ←2μ, and calculate X ⁿ⁺¹ (x, y) again ;

3) For the known X ⁿ⁺¹ (x, y), T ⁿ⁺¹ (x, y) can be obtained by regularizing the following formula after discretization:

In the formula, Indicates the operator used during iteration; if T ⁿ⁺¹ (x, y)∈T _range , take β=β ₀ and jump out of this iteration, otherwise update β←2β, and calculate T ⁿ⁺¹ (x, y) again ;

4) For a sufficiently large number n, the termination criterion is satisfied:

||(X ⁿ⁺¹ ，T ⁿ⁺¹ )-(X ⁿ ，T ⁿ )|| _D ＜ε(10);

Or if n=N _max , the iteration terminates, and (X ⁿ⁺¹ , T ⁿ⁺¹ ) is used as the final solution of the concentration field and temperature field; otherwise, update T ⁿ ←T ^{n +1} , n←n+1, and repeat steps 2 to 4 .

Step 3. In order to improve the reconstruction effect, the present invention proposes that in each direction of the region to be measured, the information containing a plurality of gas characteristic absorption lines is fully utilized, and the center frequency corresponding to the selected rth gas characteristic absorption line is recorded as is v _r . Equations (8) and (9) and (A, B) depend on v _r , so that each iteration step in Equations (8) and (9) can be used:

to replace;

Step 4. Perform grid discretization in the two-dimensional area to be measured, and use an adaptive iterative method to solve the concentration and temperature in each grid:

1) According to the shape and size of the two-dimensional area D to be measured, divide the two-dimensional area to be measured into grids of M rows and N columns, let M=N, and each grid corresponds to a concentration and temperature to be measured . Select 1 gas characteristic absorption lines from the spectral database, and I≥[2×M×N/(M+N)], the value of r is an integer between 1 and 1;

2) Formula (11.2) can be written as:

_EgS (T,vr)X=P( _vr )(13);

In the formula, P(v _r ) is the measured value projection vector corresponding to the spectral line v _r , E=(e _{(i, j)} ) is a 2N×N ² -dimensional 0-1 matrix, where e _{(i, j)} represents Whether the laser passes through the j-th grid in the i-th direction, that is, when the laser in the i-th direction passes through the j-th grid, set e _{(i, j)} = 1, otherwise e _{(i, j)} = 0;

So the explicit solution of formula (13) is expressed as:

in,

Through formula (14), X ⁿ⁺¹ (x, y) can be calculated from T ⁿ (x, y);

3) X ⁿ⁺¹ (x, y) calculated in step 2 is used as a known quantity, and T ⁿ⁺¹ (x, y) can be obtained by solving equation (12) using the nonlinear least squares optimization algorithm.

In order to ensure the numerical convergence of the iterative solution, the admissible set X _range ×T _range of X(x, y) and T(x, y) is given, so that it contains the exact solution X ^* (x, y) and T ^* (x, y), while introducing penalties with regularization parameters μ, β to overcome the ill-conditioned nature of the reconstruction process, and automatically adjust the regularization parameters μ, β in each step of iteration, so as to ensure that the iterative solution converges to the exact solution.

Simulation example

In order to test the performance of the algorithm of the present invention, the present invention simulates common temperature and concentration models in practical applications, and compares the reconstructed results of the present invention with the simulated annealing algorithm results.

The temperature range of the two-dimensional rectangular area to be measured is 1000-1500K, and the water vapor volume concentration range is 0-0.2. The distribution model adopted is a bimodal surface, and the model is constructed by superposition of a Gaussian surface and a parabolic surface. The expression is shown in the formula ( 16):

In the formula, f(x, y) is the temperature field or concentration field of the area to be measured, (x ₀ , y ₀ , z ₀ ) is the peak point position of the Gaussian surface and the parabolic surface, p ₁ , p ₂ , K, b ₁ , b ₂ , c ₁ , and c ₂ are all parameters set during simulation.

As shown in Figure 2, the area to be measured is discretized into 10×10 grids. In order to make the equations meet the closed solution conditions, the number of absorption lines selected must satisfy I≥10. Here, 10 characteristic absorption spectra of water vapor are selected. The specific information of each spectral line is shown in Table 1; the temperature field and concentration field distribution set according to the bimodal surface model are shown in Fig. 3-Fig. Field results are shown in Figures 5 to 8;

Table 1: The absorption spectrum information of 10 _H2O selected when the algorithm of the present invention carries out the simulation embodiment

From Figures 5 to 8, it can be seen that under the bimodal surface model, the temperature field and concentration field reconstructed by the alternating iterative algorithm and the simulated annealing algorithm respectively are consistent with the set values, and high reconstruction accuracy can be achieved. However, the calculation time of the alternate iterative algorithm proposed by the present invention is 6.08s, which is much shorter than the calculation time of the simulated annealing algorithm, which is 40238.33s.

In addition, there will inevitably be noise interference in the actual measurement process. In order to verify the anti-noise ability of the alternate iterative algorithm proposed by the present invention, different proportions of Gaussian white noise are added to the projected absorption area obtained by the bimodal surface model, and the temperature field and concentration field are reconstructed by using the noise-added data. In order to facilitate the comparison of reconstruction results, the root mean square error is defined as the evaluation basis:

In the formula, f _{i, j} is the temperature value or concentration value at the jth grid in the i-th direction, and f _{0(i, j)} is the set value corresponding to f _{i, j} . The root mean square error of the reconstruction is shown in Figure 9. It can be seen from Figure 9 that the alternate iterative algorithm is relatively stable when reconstructing the temperature field, and its anti-noise ability is significantly higher than that of the simulated annealing algorithm. Comprehensively considering the overall effect of reconstructing the temperature field and the concentration field, the alternate iterative algorithm proposed by the invention has strong anti-noise ability while ensuring the reconstruction quality, and is suitable for large-scale field inversion calculation.

The algorithm of the present invention first proposes a linearization scheme for the calculation of the concentration field, and semi-linearizes the original system, thus weakening the nonlinearity of the original system; secondly, an alternate iteration scheme is proposed for the measured temperature field and concentration field, and each iteration is reduced by half The number of unknown variables; finally, the optimization technique is used to introduce a penalty term to overcome the ill-conditioned nature of the reconstruction process, and the regularization parameters can be automatically adjusted at each iteration to ensure that the iterative solution converges to the exact solution. The alternate iterative algorithm proposed by the invention can significantly shorten the calculation time under the premise of maintaining the reconstruction accuracy, and is suitable for large-scale field inversion calculation.

Claims (4)

1. An alternate iterative algorithm based on spectral absorption temperature field and concentration field reconstruction, is characterized in that, comprises the steps: Step 1. The high-temperature gas to be measured flows through a two-dimensional rectangular area, and the area to be measured is recorded as D={(x, y): 0<x<L, 0<y<W}, and the temperature field is T(x, y ), the concentration field is X(x, y), the relationship between the measured value of the laser passing through area D and the temperature field and concentration field in area D is expressed by formula (1): $\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; P</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; P</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ where A(y ₀ , v ₀ ) is the measured value of the integrated absorption area of the incident laser with center frequency v ₀ along the path y=y ₀ ∈ (0, W), B(x ₀ , v ₀ ) is the x = x ₀ ∈ (0, L) integral absorption area measurement, P is the gas pressure on region D, S(T(x, y ₀ ), v ₀ ) is the temperature T(x, y ₀ ), the intensity of the spectral line at frequency v ₀ ; Step 2. Solve (X(x, y), T(x, y)) according to formula (1): 1) Assume that (X ^* (x, y), T ^* (x, y)) is an exact solution that satisfies the system, and give (X ^* (x, y), T ^* (x, y)) a prior Proximity And the initial value of iteration (X ⁰ (x, y), T ⁰ (x, y)), and give the maximum number of iterations N _max , regularization parameter μ, β>0, iteration termination level ε>0 and the allowable set X _range ×T _range , set the initial value of n to 0; 2) For the known T ⁿ (x, y), X ⁿ⁺¹ (x, y) can be obtained by regularizing the following formula after discretization: ${\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2.1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ $\left\{\begin{array}{c}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2.2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ In the formula, Indicates the operator used during iteration; if X ⁿ⁺¹ (x, y)∈X _range , take μ=μ ₀ and jump out of this iteration; otherwise update μ←2μ, and calculate X ⁿ⁺¹ (x, y) again ; 3) For the known X ⁿ⁺¹ (x, y), T ⁿ⁺¹ (x, y) can be obtained by regularizing the following formula after discretization: ${\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3.1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ $\left\{\begin{array}{c}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3.2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ In the formula, Indicates the operator used during iteration; if T ⁿ⁺¹ (x, y)∈T _range , take β=β ₀ and jump out of this iteration, otherwise update β←2β, and calculate T ⁿ⁺¹ (x, y) again ; 4) For a sufficiently large number n, the termination criterion is met: ||(X ⁿ⁺¹ ，T ⁿ⁺¹ )-(X ⁿ ，T ⁿ )|| _D ＜ε(1); or n=N _max , the iteration terminates, and (X ⁿ⁺¹ , T ⁿ⁺¹ ) is used as the final solution of the concentration field and temperature field; otherwise, update T ⁿ ←T ⁿ⁺¹ , n←n+1, and repeat step 2)～ 4). 2. according to claim 1, the alternating iterative algorithm based on the temperature field and concentration field reconstruction of spectral absorption is characterized in that, on each direction of region to be measured, make full use of the information that comprises a plurality of gas characteristic absorption lines, will The center frequency corresponding to the selected rth gas characteristic absorption line is denoted as v _r , so formula (2.1), formula (2.2), formula (3.1) and formula (3.2) use formula (5.1) and formula (5.2) respectively , Equation (6.1) and Equation (6.2) replace: ${\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5.1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ $\left\{\begin{array}{c}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5.2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ ${\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6.1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ $\left\{\begin{array}{c}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6.2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$ 3. according to claim 2, based on the alternating iterative algorithm of temperature field and concentration field reconstruction of spectral absorption, it is characterized in that, carry out grid discretization processing in the area to be measured, and adopt self-adaptive iterative method to solve each grid concentration and temperature, the solution process is: 1) According to the shape and size of the two-dimensional area D to be measured, divide the two-dimensional area to be measured into grids of M rows and N columns, let M=N, and each grid corresponds to a concentration and temperature to be measured , select I gas characteristic absorption line from spectral database, and I≥[2×M×N/(M+N)], the value of r is an integer between 1 and 1; 2) Formula (5.2) is written as: EgS(T,v _r )X=P(v _r )(7); In the formula, P(v _r ) is the measured value projection vector corresponding to the spectral line v _r , E=(e _{(i, j)} ) is a 2N×N ² -dimensional 0-1 matrix, where e _{(i, j)} represents Whether the laser passes through the j-th grid in the i-th direction, when the laser in the i-th direction passes through the j-th grid, set e _{(i, j)} = 1, otherwise e _{(i, j)} = 0; The explicit solution of formula (7) is expressed as: ${\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ in, Through formula (8), X ⁿ⁺¹ (x, y) can be calculated from T ⁿ (x, y); 3) X ⁿ⁺¹ (x, y) calculated from step 2) is used as a known quantity, and T ⁿ⁺¹ (x, y) can be obtained by solving formula (6.1) using nonlinear least squares optimization algorithm. 4. The alternate iterative algorithm for rebuilding temperature field and concentration field based on spectral absorption according to claim 1, characterized in that: given X (x, y) and T (x, y) allowable set X _range × T _range , so that it contains the exact solutions X ^* (x, y) and T ^* (x, y), and at the same time introduces a penalty term with regularization parameters μ, β to overcome the ill-conditioned nature of the reconstruction process, and automatically Adjust the regularization parameters μ, β to ensure that the iterative solution converges to the exact solution.